\left\{ \begin{array} { l } { a _ { 1 } q ^ { 2 } = \frac { 5 } { 2 } } \\ { a _ { 1 } + a _ { 1 } q + a _ { 1 } q ^ { 2 } = \frac { 15 } { 2 } \quad q = \frac { 5 - a _ { 1 } } { a _ { 1 } } } \end{array} \right.
Evaluate
a_{1}q^{2}=\frac{5}{2},\ a_{1}q^{2}+a_{1}q+a_{1}=\frac{15q}{2}\text{ and }\frac{15q}{2}=-1+\frac{5}{a_{1}}
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